Formation of weakly bound molecular complexes: ( $$^3$$ 3 He) $$_2$$ 2

Abstract

Experimental evidence for low-temperature (exothermic) atom-exchange chemical reactions was recently reported after starting with an optically trapped near-quantum-degenerate gas of polar $$^{40}$$ K $$^{87}$$ Rb (fermionic) molecules prepared in their absolute ground state. Here we demonstrate the similar fermionic ( $$^3$$ He $$^3$$ He) molecules formation via vacancies in quantum $$^4$$ He crystal. A quantum crystal is defined as one in which the energy of the zero-point oscillations of each atom is not small in comparison with the depth of the potential well in which the atom is located (or mathematically $$\Lambda \equiv (\hbar /a\sqrt{m\,E_i})\ge 1$$ ; m is the mass of an atom, $$E_i$$ is the characteristic interaction energy of the atoms, and a is the interatomic distance). Our modified Gross–Pitaevskii approach, based on the extention to Anderson’s adopting Gross–Pitaevskii equation for treating dilute vacancies, supplies in particular the zero-energy limit of the wave function (and the extra energy caused by the curvature of the wave function) for investigations of possible formation of ( $$^3$$ He) $$_2$$ molecules bound by the elastic deformation field around the isotopic impurities as well as bound states (scattering resonances) for a $$^3$$ He-vacancy system in crystalline $$^4$$ He.